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18 Jul 2018, 19:50
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:35) correct
36%
(02:44)
wrong
based on 291
sessions
History
Date
Time
Result
Not Attempted Yet
How many numbers between 1 and 200 are exactly divisible by exactly two of 3, 9 and 27?
a. 14
b. 15
c. 16
d. 17
e. 18
a. 14
b. 15
c. 16
d. 17
e. 18
18 Jul 2018, 20:13
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GoonerForever
Anything divisible by 27 will be div by 3 and 9 also...
Anything divisible by 9 is also divisible by 3,
SO we look for multiple of 9 till 200, but these should not be divisible by 27..
Multiples of 9 till 200 = 200/9=22.xy, so 22 multiples
Multiples of 27 till 200= 200/27=7.xy, so 7 multiples
Therefore answer = 22-7=15
B
General Discussion
18 Jul 2018, 21:15
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I used part of the triple venn diagram formula to solve this...
we need how many numbers in the given range are divisible by all three 3, 9 and 27...
LCM of 3, 9 and 27 is 27
formula to know how many multiples of 27 in the range
last multiple of 27(in the range)-[first multiple of 27(in the range)/ 27] + 1
(189-27/27) + 1 = 7
How many numbers between 1 and 200 are exactly divisible by exactly two
ie
1) 3 and 9
2) 9 and 27
and 3) 27 and 3
1) 3 and 9 ... LCM is 9
applying same formula as above
total number of multiples of 9 is 22
2) 9 and 27...LCM is 27
total number of multiples of 27 in range is 7
3) 9 and 3...LCM is 27
total number of multiples of 27 in range is 7
to know the multiples in exactly 2 of the divisors we need to subtract the the number of multiples of all 3 divisors from each
therefore: (22-7) + (7-7) + (7-7) = 15
we need how many numbers in the given range are divisible by all three 3, 9 and 27...
LCM of 3, 9 and 27 is 27
formula to know how many multiples of 27 in the range
last multiple of 27(in the range)-[first multiple of 27(in the range)/ 27] + 1
(189-27/27) + 1 = 7
How many numbers between 1 and 200 are exactly divisible by exactly two
ie
1) 3 and 9
2) 9 and 27
and 3) 27 and 3
1) 3 and 9 ... LCM is 9
applying same formula as above
total number of multiples of 9 is 22
2) 9 and 27...LCM is 27
total number of multiples of 27 in range is 7
3) 9 and 3...LCM is 27
total number of multiples of 27 in range is 7
to know the multiples in exactly 2 of the divisors we need to subtract the the number of multiples of all 3 divisors from each
therefore: (22-7) + (7-7) + (7-7) = 15
